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1/1x2+1/2x3+1/3x4+.......1/99x100

解: 1/1X2+1/2X3+1/3X4+...+1/99X100 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100) =1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100 (中间两项两项正负抵消) =1-1/100 =99/100

1/1x2+1/2x3+1/3x4+......+1/99x100 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/99-1/100) =1-1/2+1/2-1/3+1/3-1/4+......+1/99-1/100 =1-1/100 =99/100

原等式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/98-1/99)+(1/99-1/100)=99/100

K>99? s=s+1/((k*(k+1)) 第二个空中的外层括号为了表示更清楚,代表k*(k+1)在分母上,填空时省略外层括号

1/n(n+1)=1/n-1/(n+1) 1/1×2=1-1/2 1/2×3=1/2-1/3 .... 1/99×100=1/99-1/100 都加一起右边=1-1/2+1/2-1/3+1/3......-1/100 =1-1/100=99/100

1/1x2+1/2x3+1/3x4+······+1/99x100=1-1/2+1/2-1/3+1/3-.....-1/99+1/99-1/100=1-1/100=99/100

可以收图吗

1/(1x2)+1/(2x3)+1/(3x4)……1/(98x99)+1/(99x100) =(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/98-1/99)+(1/99-1/100) =1-1/2+1/2-1/3+1/3-1/4+……+1/98-1/99+1/99-1/100 =1-1/100 =99/100

1X2分之1+2X3分之1+3X4分之1......+98X99分之1+99X100分之1 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/98-1/99)+(1/99-1/100) =1-1/100 =99/100

裂项法: 1/1x2十1/2x3十1/3x4十…十1/98x99十1/99x100 =1-1/2+1/2-1/3+1/3-1/4+……+1/98-1/99+1/99-1/100 =1-1/100 =99/100

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